1. Field of the Invention
The present invention relates to a method and an apparatus for measuring the lifetime of minority carriers in a semiconductor.
2. Description of the Related Art
Examination of lattice defects in a semiconductor is one of the important tests to be performed during semiconductor circuit manufacturing because lattice defects have a great influence on the electrical characteristics of the semiconductor. Since the lifetime of minority carriers in a semiconductor is strongly correlated to the density of the lattice defects, minority carrier lifetime is measured in order to evaluate the lattice defects. Conventionally, the so-called Zerbst method is used to measure the minority carrier lifetime. The Zerbst method is described in Phys., vol. 22, p. 30, 1966, by M. Zerbst and Z. Agnew, and also in "The Pulsed MIS Capacitor," Phys. Stat. Sol., Vol. (a)89, pp. 13-43, 1985, by J. S. Kang and D. K. Schroeder, which are expressly incorporated by reference herein.
FIGS. 8A through 8C schematically illustrate a method of measuring capacitance-transient characteristics, and deriving a C-t curve, according to the Zerbst method. In FIG. 8A, a semiconductor wafer 100 has a substrate 101 and an insulating film 102, or an oxidation film, formed on a surface of the substrate 101. A first electrode 200 is formed on the insulating film 102, so as to constitute a metal-insulator-semiconductor (MIS) diode. A second electrode 210 is formed on the other surface of the substrate 101. According to the Zerbst method, a high frequency voltage with a bias is applied between the first and the second electrodes 200 and 210 by an electrical power supply 300. The bias voltage is changed stepwise as shown in FIG. 8B, and a time-dependent change of the capacitance of the MIS diode, i.e. a C-t curve, is measured as shown in FIG. 8C. The minority carrier lifetime in the substrate 101 is determined through the analysis of the C-t curve.
The capacitance change of the MIS diode during the measurement is given by the following equation: ##EQU1## wherein the symbols denote: q: Elementary charge of an electron
Nd: Impurity density PA0 .epsilon.o: Permittivity in vacuum PA0 .epsilon.s: Dielectric constant of semiconductor PA0 Cox: Capacitance of insulating film PA0 C: Total capacitance of MIS diode PA0 Cinv: Total capacitance of MIS diode under inversion conditions PA0 ni: Intrinsic carrier density PA0 .tau.g: Minority carrier lifetime PA0 s: Surface recombination Rate
Equation (1) shows that a plot of the rate of change of (Cox/C).sup.2 versus the value of ((Cinv/C)-1) will be a straight line. The gradient of the plotted straight line includes the minority carriers lifetime .tau.g, as the only unknown parameter. The minority carrier lifetime .tau.g is therefore calculated from the gradient of the straight line, which is obtained by the C-t curve measurement.
FIG. 9 is a graph showing C-t curves obtained by the conventional Zerbst method. In the examples of FIG. 9, it takes about ten minutes to measure one C-t curve. The measurement time can be shortened by reducing the bias voltage. However, as the bias voltage is reduced, the recombination of minority carriers at the insulating film-substrate interface will dominate, in the recombination processes of the minority carriers, thereby increasing the significance of the second term on the right-hand side of Equation (1), that is, (qsni). The increase of the term (qsni) obscures the linearity between the rate of change of (Cox/C).sup.2 and the value of ((Cinv/C)-1), thus making it difficult to evaluate the minority carrier lifetime correctly.